论文标题
$α$ -Euler方程的限制$α\至0 $在半平面中，没有滑移边界条件和涡流表初始数据
The limit $α\to 0$ of the $α$-Euler equations in the half plane with no-slip boundary conditions and vortex sheet initial data
论文作者
论文摘要
在本文中，我们研究了$α\至0 $的溶液在半平面中$α$ - 欧拉群体系统的限制，具有无滑边界条件，对2D不可压缩的Euler方程的解决方案弱的解决方案在$ h^{-1} $中的界面radon量度中具有非阴性初始涡度。该结果扩展了在ARXIV中进行的分析：1611.05300和ARXIV：1403.5682。它需要一种基本不同的方法，类似于用于DELORT定理的方法，以及对半平面（无滑动）过滤速度和潜在涡度之间关系的新详细研究。
In this article we study the limit when $α\to 0$ of solutions to the $α$-Euler system in the half-plane, with no-slip boundary conditions, to weak solutions of the 2D incompressible Euler equations with non-negative initial vorticity in the space of bounded Radon measures in $H^{-1}$. This result extends the analysis done in arXiv:1611.05300 and arXiv:1403.5682. It requires a substantially distinct approach, analogous to that used for Delort's Theorem, and a new detailed investigation of the relation between (no-slip) filtered velocity and potential vorticity in the half-plane.
